﻿using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ProjectEulerSolutions
{
    /*
     * A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
        a^2 + b^2 = c^2

        For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.

        There exists exactly one Pythagorean triplet for which a + b + c = 1000.
        Find the product abc.

     * */
    class Problem9
    {
        public static string Calculate()
        {
            string result = "";

            for (int c = 1000; c >= 0; c--)
            {
                for (int b = 1; b < 1000 - c; b++)
                {
                    int a = 1000 - b - c;
                    if (a < b)
                        if (a * a + b * b == c * c)
                        {
                            result = (a * b * c).ToString();
                            Console.WriteLine(a * b * c);
                        }
                }
            }

            return result;
        }
    }
}
